Bit-Flip Count Table - Quantum Computing Physical Bases: Control, Coupling, and Error Signals Step by Step

A bit-flip table turns prepared labels into visible rows of stays and flips: prepared zero has 18 stays and 2 flips, while prepared one has 3 flips and 17 stays. The lesson treats those counts as exact model inputs so the channel arithmetic is exact for this table, but a real device would estimate the rows from finite shots with uncertainty.

A classical error channel is built from exact prepared-label counts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

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Counts define a classical error channel

Prepared zero gives 18 stays and 2 flips. Prepared one gives 3 flips and 17 stays.

\text{zero row }(18,2),\quad \text{one row }(3,17)

Prepared-label rows expose both error rates

The channel has a zero-prepared row, a one-prepared row, and a conserved row sum.

\begin{array}{c|c|c}\text{prepared}&p_{\text{zero}}&p_{\text{one}}\\\text{zero}&\frac{9}{10}&\frac{1}{10}\\\text{one}&\frac{3}{20}&\frac{17}{20}\\\text{row sum}&1&1\\\end{array}

The channel changes the count budget

The ideal true budget maps to observed counts 57 and 23 over 80 shots.

N_{\text{zero}}=57,\quad N_{\text{one}}=23